Behavioral dynamic portfolio selection with S-shaped utility and epsilon-contaminations

Inspired by the classical cumulative prospect theory (CPT), we propose a CPT-like functional characterized by the modeling of uncertainty on gains and losses through two epsilon-contaminations of a reference probability measure. Such functional is used to perform a dynamic portfolio selection in a finite horizon binomial market model, reducing it to an iterative search problem over the set of optimal solutions of a family of pairs of non-linear optimization problems on the final wealth. Despite the computational hardness of the resulting pairs of problems, epsilon-contaminations allow to represent each solution in terms of the partition generated by the stock price random variable at maturity, obtaining a sensible reduction of variables and constraints. In turn, the optimization task can be reduced to the maximization of a real-valued function of one real variable, revealing the possible ill-posedness of the problem. The resulting model is discussed by means of some paradigmatic examples on market data and a sensitivity analysis.